Block #123,052

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/18/2013, 8:18:23 PM · Difficulty 9.7605 · 6,672,395 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

83445e4e444486edaa557ea431da6bfb68ec53628897e693b092e8e22bed9ffa

View on Chainz ↗

Height

#123,052

Difficulty

9.760533

Transactions

Size

620 B

Version

Bits

09c2b24c

Nonce

239,874

Timestamp

8/18/2013, 8:18:23 PM

Confirmations

6,672,395

Mined by

⛏️ P2SHARni8u3hvGNqrxiVbw1sYz4rzqNDdpsbod

Merkle Root

399cc1d3c558415962a79963e2162a4ded8b26341a884c7f35771ed84fd3a311

Transactions (3)

Coinbase6a4cd2b0275071…773e45a47f1dd8

1 in → 1 out10.5000 XPM109 B

ARni8u3h…NDdpsbod

1c939bf924bd56…8c1ea58732a82a

1 in → 2 out10.4900 XPM192 B

AYs3x9NT…V2hAhoH8 AXUtFnVB…2K4kmJnq

6c7bb5044ccb81…fdec6990cdd813

1 in → 2 out2.1634 XPM227 B

ANN8gjLH…8ToruqzW AMTxuc2Q…Goh59Bwc

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.215 × 10⁹⁹(100-digit number)

72158704383841226214…74718291679796228959

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

7.215 × 10⁹⁹(100-digit number)

72158704383841226214…74718291679796228959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.443 × 10¹⁰⁰(101-digit number)

14431740876768245242…49436583359592457919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.886 × 10¹⁰⁰(101-digit number)

28863481753536490485…98873166719184915839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.772 × 10¹⁰⁰(101-digit number)

57726963507072980971…97746333438369831679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.154 × 10¹⁰¹(102-digit number)

11545392701414596194…95492666876739663359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.309 × 10¹⁰¹(102-digit number)

23090785402829192388…90985333753479326719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.618 × 10¹⁰¹(102-digit number)

46181570805658384777…81970667506958653439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.236 × 10¹⁰¹(102-digit number)

92363141611316769554…63941335013917306879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.847 × 10¹⁰²(103-digit number)

18472628322263353910…27882670027834613759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer